Figure 1: On-chip optical nonreciprocity based on nonlinear dynamics near an exceptional point.

(a) Basic operating scheme of the proposed concept. (b) Effective index modulation profiles over the unidirectional converter region for the attenuating (upper) and amplifying (lower) waveguides. (c,d) Two-dimensional numerical calculations (FEM, Comsol Multiphysics) assuming single-mode slab waveguides with the following optical parameters: cladding index of 1.50; core index of 1.55; core index modulation depth Δncore=6 × 10−4. The effective index modulation amplitude is given by Δn0=ΓΔncore and the confinement factor is Γ=0.71. Operation at the vacuum wavelength of 1,130 nm and in the fundamental transverse-electric mode (TE0) is assumed. The colour scale indicates intensity I in dB with respect to the incident intensity I0. The peak intensity of the incident mode is I0=IS for both the forward and backward transmission cases, where IS denotes a gain saturation intensity constant. (e) Cross-sectional profiles of the transmitted intensity in the forward and backward directions. The estimated nonreciprocal transmission ratio (NTR) is 28.7 dB and the forward transmission gain is 4.95 dB.